Question

what kind of transformation is illustrated in this figure?
rotation
dilation
reflection
translation

Explanation:

To determine the transformation, we analyze each option:

• Rotation: Involves turning a figure around a point. The triangles here don't show a rotational change.
• Dilation: Changes the size of the figure. The triangles appear to be the same size, so not dilation.
• Reflection: Flips a figure over a line. The orientation and position don't suggest a reflection.
• Translation: Moves a figure without rotating, reflecting, or changing size. The triangle \(ABC\) to \(A'B'C'\) shows a horizontal/vertical shift with the same shape, size, and orientation, indicating translation.

Answer:

D. translation